Cards In This Deck

• $\text{In a regression line equation }y=a+bx\text{, how do you interpret the value of }b\text{ in context?}$
  $$\begin{gathered} b\text{ is the gradient.} \\ \text{Interpretation: For every 1 unit increase in x, the value of y changes by b.} \end{gathered}$$
• $\text{Which variable must be plotted on the }x\text{-axis of a scatter diagram?}$
  $$\begin{gathered} \text{The Independent (or Explanatory) variable.} \\ \text{This is the variable that is set or controlled by the researcher.} \end{gathered}$$
• $\text{When is a linear regression model appropriate for a set of data?}$
  $$\begin{gathered} \text{1. The scatter diagram shows a linear trend (points lie roughly along a straight line).} \\ \text{2. The PMCC (}r\text{) is close to 1 or -1.} \end{gathered}$$
• $\text{When calculating the regression line of }y\text{ on }x\text{, which variable must be the independent (explanatory) variable?}$
  $x\text{ must be the independent (explanatory) variable.}$
• $\text{What is the first step to calculate }{S}_{xx}\text{ given sum data (e.g., }\sum x\text{, }\sum x^2\text{)?}$
  $$\begin{gathered} \text{Use the summary statistic formula:} \\ {S}_{xx}=\sum x^2-\frac{(\sum x{)}^2}{n} \end{gathered}$$
• $\text{How do you interpret the value }b\text{ in the regression equation }y=a+bx\text{ in context?}$
  $$\begin{gathered} \text{It is the change in }y\text{ for every unit increase in }x\text{.} \\ \text{"For every extra [unit of }x\text{], the [variable }y\text{] increases/decreases by [}b\text{]."} \end{gathered}$$
• $\text{When is the regression constant }a\text{ (the }y\text{-intercept) physically meaningless in a real-world context?}$
  $\text{When }x=0\text{ lies far outside the range of the observed data, or when having }x=0\text{ is impossible in reality (e.g., height of a human with age 0).}$
• $$\begin{gathered} \text{True or False?} \\ \text{The regression line of }y\text{ on }x\text{ (}y=a+bx\text{) can be used to predict a value of }x\text{ given a value of }y\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{This line is specifically minimized for vertical distances (errors in }y\text{). } \\ \text{To predict }x\text{ from }y\text{, you would need to calculate the regression line of }x\text{ on }y\text{ (which is a different line), or rearrange the formula algebraically (though this is less accurate than the proper }x\text{ on }y\text{ line).} \end{gathered}$$
• $\text{When is a prediction made using a regression line considered reliable?}$
  $\text{When the value of the independent variable (}x\text{) used for prediction lies within the range of the original data (Interpolation).}$